Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang

2022/03/31 by Gargi Mukherjee, Mukherjee, Gargi · 1 citation
Mathematics · #Mathematical Approximation and Integration #Analytic Number Theory Research #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2204.00055

Abstract

Let p(n) denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., (-1)^r-1Δ^r log \p(n), by studying the inequality of the following form log (1+\dfracC(r)n^r-1/2-\dfracC₁(r)n^r)

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• Asymptotics of the shifted finite differences of the overpatition function and a problem of Wang--Xie--Zhang

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